We consider a problem of searching optimal control inputs of a system in which the input-output relation is prescribed by a nonlinear function with unknown characteristics. In such a system, if output values corresponding to all input values are observed, the input-output relation can be completely known and so optimal input values can be found. But it may be impossible in practice when the number of input values is indefinitely, many. In this case a random search method is considered to be a useful method for searching approximate optimal values.
For this problem, in this paper, a learning algorithm of the random search is presented. Each time, under this scheme, an input is chosen probabilistically and its response from the system is observed. The probability of choosing an input is changed according to its response by a learning manner of trial and error. It is shown that under this scheme the probability of choosing an optimal input converges to unity within arbitrary accuracy as search time evolves. Furthermore, practical availability of this algorithm is revealed by applying it to problems of equation solving and traverser control.